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arXiv · 1005.5195

Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions

B. Pirvu·F. Verstraete·G. Vidal
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Abstract

We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain of N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D^3, where g(D,ξ/N) is a nontrivial function. For ξ<< N, this scaling reduces to D^3, independent of the system size N, making our algorithm N times faster than previous proposals. We apply the method to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.

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B. Pirvu, F. Verstraete, G. Vidal. 2010-05-27. Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions. https://doi.org/10.1103/physrevb.83.125104

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